Game of strategy - Ch 14 solutions PDF

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Solutions to Chapter 14 ExercisesSOLVED EXERCISESS1. (a) In the pure-threat case, the union’s expected payoff is 50(1 – p) – 100p = 50 – 150p. The union’s expected payoff goes to zero for p = 1/3 and is negative for p > 1/3. Thus the pure threat is too big from the union’s perspective. There ...

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Solutions to Chapter 14 Exercises SOLVED EXERCISES

S1.

(a)

In the pure-threat case, the union’s expected payoff is 50(1 – p) – 100p = 50 – 150p. The

union’s expected payoff goes to zero for p = 1/3 and is negative for p > 1/3. Thus the pure threat is too big from the union’s perspective. There may be scope for brinkmanship in this case. (b) Diagram is given below:

(c)

The union sets up a situation in which there is some risk, with probability q, that the

company’s defiance will lead to a damaging strike. (d)

If brinkmanship is used, a profitable company is better off conceding to the union

demands if 50 > – 100q + 100(1 – q), or q > 1/4. This is the effectiveness condition. With brinkmanship, the union’s expected payoff is 50(1 – p) – 100qp. Brinkmanship is acceptable to the union if this payoff is positive, or if q < (1/2)(1 – p)/p. This is the acceptability condition. The union will use the pure threat ( q = 1) for p < 1/3. For values of p between 1/3 and 2/3, the union can successfully use brinkmanship. For values of p > 2/3, the union uses no threat at all.

S2.

(a)

This scene makes the escalation of risk inherent in brinkmanship explicit. If both players

continue on their set paths—the army officer in raising the helicopter and the gunman in refusing to provide information—they raise the risk that the gunman dies on the next push out of the helicopter. Then neither side gets what it wants. As in other examples of brinkmanship, each is feeling the other out for his level of risk tolerance. (b)

In this film, the FBI agent makes explicit a probabilistic threat that spending any of the

found ransom money may lead to Hank’s arrest. Given this information, Hank must determine his own

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willingness to spend the money, knowing that increases in spending increase the risk that his crime will be discovered. Although the threat is presumably acceptable to the FBI, it remains to be seen whether it will be effective in deterring Hank’s spending the money.

S3.

The examples described in this exercise (and in Exercises S4 and S5) do not have unique,

mathematically correct answers; their purpose is to get students thinking about real-world issues using gametheoretic perspectives. Each is so complex and rich in factual detail that setting the stage completely would take several pages. Therefore, we offer only the basic facts of each, with some suggestions for your further analysis. Each topic can develop in many different directions and can benefit from factual information or experience that you may be able to contribute. (a)

THE URUGUAY ROUND OF TRADE NEGOTIATIONS

General trade liberalization brings overall economic benefits to all countries. But within each country there are gainers and losers; people whose incomes are tied to the export sectors gain as more and bigger markets open up for them, and those whose incomes are tied to the import sectors lose as they must face stiffer competition from other countries’ products. Thus almost no country can present a clear and unified front for trade liberalization; each must resolve its internal conflict over the gains and losses. In the Uruguay Round, one can identify three main parties or groups of nations: 1.

The United States’ main interest was to achieve liberalization of the markets for its traditional (agriculture) and emerging (especially high technology, including high-tech services like banking and insurance) export sectors, to obtain more open and liberal treatment of direct investment by multinationals and to ensure that other countries protect intellectual property rights (patents and copyrights). But the United States also wanted to protect its politically sensitive sectors, such as autos, steel, and textiles.

2.

Japan and Europe wanted to protect their farmers and traditional manufacturing industries but had some interests in common with the United States in liberalizing high-tech trade.

3.

The developing countries wanted to protect and promote their own fledgling high-tech and service sectors but to get access to the developed countries’ markets in textiles, traditional manufacturing sectors, and so on. There was also the general view that the General Agreement on Tariffs and Trade (GATT) was ineffective in enforcing its agreements. The procedure to investigate a complaint that one country was restricting its imports in violation of its GATT obligations was slow; the guilty country could veto the findings of the investigating panel and could stall and delay the imposition of any sanctions almost indefinitely.

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Successful conclusion of the negotiations in such a forum needs near unanimity; therefore, each group could threaten to cause the talks to collapse. If this meant merely continuation of all the liberalizing agreements reached under the previous rounds of GATT, the threat was not too severe. However, if the failure of the Uruguay Round could worsen matters to a point where countries fell into blocs that raised their trade barriers against each other, a harmful trade war could break out. The Uruguay Round was launched in 1986 with an extremely ambitious agenda that included all the items listed above—services, intellectual property rights, investment, agriculture, and so on—and plans to tighten GATT’s procedures for settling disputes among member countries. The negotiations stalled at several points, most critically on the issue of agriculture. The whole effort seemed doomed to failure, especially in 1993, when the fast-track legislation—which enabled the U.S. administration to enter into the negotiations and make a credible deal—was about to expire. Under this deadline, a compromise settlement was reached. It included many of the very ambitious items of the initial agenda and the formation of a new international organization, the World Trade Organization. A key provision was the single-package idea, whereby countries had to sign on to the whole package of rules and procedures; they were not allowed to accept only those provisions that suited them and opt out of the others. The hope was that each country would find the package as a whole sufficiently in its interest to join when the only alternative was to stay outside. But the risk was that if one large country chose to stay outside (as the United States did in the case of the League of Nations after the First World War and of the International Trade Organization after the Second), then the effectiveness of the whole organization would be greatly reduced. (b)

THE CAMP DAVID ACCORDS

By the mid-1970s, the prospects for peace in the Middle East looked bleak. Israel had captured a large amount of territory in the Six-Day War of 1967: the Sinai Peninsula from Egypt, the West Bank and East Jerusalem from Jordan, and the Golan Heights from Syria. The defeat in this war humiliated the Arab countries and made them even more unwilling to negotiate with Israel or accept its existence. The SixDay War also greatly increased the population of Palestinians living in exile in various Arab countries. These exiles grew more militant and even violent in their opposition to any deal with Israel and in their insistence on the establishment of a Palestinian state in some or even all of the land of Israel. In the Yom Kippur War of 1973, the Arab countries acquitted themselves better and won back some confidence and self-respect. This raised the prospects of moves toward peace, but little progress was being made. The best prospect was that of a deal between Israel and Egypt. Indeed the two had negotiated some very limited disengagements in the Sinai in 1973 and 1975. In the longer run, Israel’s main objective was to achieve a durable peace, combined with recognition from one or more Arab states. It was willing to give up in exchange some of the land it had captured in the Six-Day War of 1967. But there were large political divisions within Israel on this issue. The Golan Heights had military importance, the West Bank was regarded as an integral part of the historic land of Israel by a large proportion of the

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population, and almost no Israeli was willing to give up East Jerusalem. Sinai was the most promising candidate for a land-peace trade. Egypt attached considerable importance to getting the Sinai back. But it also wanted to maintain a leadership role in the Arab world. A separate peace, especially one involving any formal diplomatic recognition of Israel, would cost Egypt and its leadership dearly in the Arab world and within Egypt itself. (Indeed, Anwar Sadat was assassinated a few years later.) If Egypt could secure a settlement of the Palestinians’ claims that was acceptable to them and their leaders, that might be quite a coup. However, this settlement was difficult to attempt, since the Arab states had designated the Palestine Liberation Organization (PLO) “the sole legitimate representative” of the Palestinian people. It was also a very long shot. This was the background in the summer of 1977, when President Jimmy Carter initiated a direct involvement of the United States as an intermediary between Israel and Egypt, and possibly also other Arab countries and the PLO. He and his diplomats held separate meetings with the various parties in Washington and other venues. The aim was to set up direct negotiations in Geneva. But talks stalled because of some unresolvable opposition in the United States and the Arab countries and some mishandling that lost control of the diplomatic process. Then in November 1977, the Egyptian president, Anwar Sadat, attempted a dramatic breakthrough with a trip to Jerusalem; in December, Israeli prime minister Menachem Begin made a reciprocal trip to Ismailiya. Begin offered some ideas on home rule for the Palestinians in the West Bank but no withdrawal or territorial concessions. In early 1978, Carter began another round of discussions in an attempt to bring the two sides together. Little progress was made; in particular, Begin proved totally inflexible on the land question and adamant on other matters as well. In July 1978, with the process near collapse, Carter decided to attempt a breakthrough summit meeting with Sadat and Begin at the official presidential retreat, Camp David, isolated in the Maryland mountains. These meetings were held on September 5 to 17, 1978. Neither side knew for sure how much weight the other placed on achieving a compromise. Using brinkmanship, each could explore the other’s willingness to compromise while trying to get a better deal for itself. The threat was the risk of collapse of the negotiations, which in turn could have worsened the relationship between the two and even led to another war. Each side could use its internal divisions to make this risk more credible. The situation met all the conditions for use of brinkmanship that we have studied in this chapter. An additional complication was that Sadat and Begin did not get along at all on a personal level. But there was also a game involving Carter, who by his active involvement and by convening such a high-level, high-visibility meeting, had put a lot of U.S. prestige on the line. Failure of the meeting would have been seen as a failure of U.S. diplomacy and would have caused significant damage to future U.S. involvements in international affairs. Therefore, the United States was willing to contribute something from the outside, mainly economic aid, to achieve agreement. The Israeli and Egyptian

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governments both knew this, so they could also tacitly collude to practice brinkmanship against the United States to obtain more aid, again using the risk of collapse as a brinkmanship threat. After 10 days of exchanging proposals that embodied largely entrenched positions, and offers of compromise only on issues that mattered relatively less to the other side, an impasse seemed to have been reached. At different points Sadat and Begin each threatened to walk out. Carter told Sadat that if he left, “it would mean an end to the relationship between Egypt and the United States.” There were no similar direct threats to Begin, presumably for reasons of internal U.S. politics, but Carter was preparing a joint statement with Sadat that would blame Begin for the collapse should this occur. Finally, on September 17, accord was reached on several issues, and the parties agreed to declare the summit a success, leaving other issues to be resolved later. It transpired that Sadat valued the return of Sinai more than the settlement of the Palestinian question, and Begin did not regard a collapse of the talks as such a bad outcome. According to William B. Quandt, Begin “knew how to play the game of brinkmanship, holding back on his final concessions until everyone else had put his cards face up on the table” (Peacemaking and Politics [Washington, D.C.: Brookings, 1986]). Therefore, Israel got the best deal out of Camp David. It agreed to give up all of Sinai but did not make any concessions on the West Bank or Gaza. In return Israel got normalization of relations with Egypt (and in 1979 a full peace treaty and establishment of diplomatic relations). And although this was not an explicit written part of the agreement, both Egypt and Israel got substantially increased U.S. aid.

S4.

(a)

THE BEIJING MASSACRE

After the death of Mao Zedong and the advent of Deng Xiaoping to supreme power in the late 1970s, China embarked on a remarkable program of economic liberalization, especially in agriculture. But the political dominance of the Communist Party, aided by the army, remained unchallengeable. The regime was somewhat less harsh than under Mao. Occasional voices of dissent, such as the posters on the Democracy Wall in 1978–1979, were briefly tolerated, but even this movement was eventually suppressed and its leaders jailed. As information about the rest of the world became more easily accessible, a group of students began to yearn for greater political freedom and wanted to move China toward a more open and democratic system. The governing elites, comprising the Communist Party and the military, wanted to maintain their control and power. Therefore, they saw the democracy movement as a major political challenge, even though they had given up much of the socialist economic ideology of the Marxist-Leninist-Maoist variety. The government was somewhat concerned about world opinion; it would have preferred a peaceful end to the students’ protest and probably would have made some minor concessions to achieve this. Thus a violent suppression of the student protests would be very costly to both sides. But the students did not

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know the relative weights the government placed on its two aims—the maintenance of power and the peaceful resolution of the situation. In fact, the leadership in the government was not united. President Zhao Ziyang was somewhat sympathetic to the students, whereas Prime Minister Li Peng was a hardliner. Most of the others were octogenarians of the old guard and inclined to a hard line. Most important, so did Deng, who was still the de facto dictator even though the only formal title he held was honorary chairman of the China Bridge Club. The immediate trigger for the student protests in spring 1989 was the death on April 15 of the former prime minister Hu Yaobang. Hu had liberal tendencies and had been ousted by hard-liners two years earlier, thereby acquiring something of a hero status among the students. Posters mourning the death of Hu began to appear at Beijing University; gradually the posters became bolder in criticizing Deng and demanding reforms. On April 27 the students staged a huge march to Beijing’s Tiananmen Square, which is at the center of the government’s offices and the top leadership’s homes, and back. Troops tried to stop them but did not use force when the students broke through; it seems this was because the top leadership failed to give any explicit or detailed order to the commander of the troops. The students and members of the public who supported their aims were emboldened by this. Some students began a hunger strike for their demands. They conducted the strike in Tiananmen Square, which gradually became the site of a permanent large gathering and demonstration. The students were further emboldened by a visit by Mikhail Gorbachev, whom they admired for his economic and political liberalization of the Soviet Union. The government imposed martial law on May 19, and the liberally inclined Zhao Ziyang was confined to his house. The hard-liner Li Peng made some threatening speeches, but there was no immediate attempt to drive the students from Tiananmen Square. More troops arrived on the scene, and the students disabled some army vehicles and even took some weapons. This combination of harsh noises and lack of firm action from the government further emboldened the extremists among the students; the demonstrations grew in size, intensity, and demands. Finally, during the night of June 3–4, troops attacked the demonstrators, shooting and killing many of them. The numbers killed may have reached thousands. The demonstration was suppressed and the leaders given harsh prison terms. (b)

THE CATERPILLAR STRIKE

The wages that striking workers lose for the duration of a strike generally exceed the extra gains they make at the settlement of the strike, compared with the last offer they rejected when commencing the strike. Thus it is generally not an optimal choice for a labor union to call its members out on a strike. The company stands to lose much of its production and profit in a strike, too. Thus a strike can be a valuable strategy in its role as a threat—an attempt to compel the company to increase its offer of wages, working conditions, or other contract terms. An actual strike is a failed threat— one that has failed to achieve its purpose. If this is true of strikes in general, then a strike that lasts seven years and leaves the workers in severe financial, social, and emotional troubles must count as a threat that

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was too large to make. But it might have been rational to attempt brinkmanship by creating a risk of this drastic outcome. The strike of the United Auto Workers against Caterpillar, which went on intermittently for seven years, must belong to this category. Caterpillar, the United States’ largest manufacturer of construction equipment, was facing increasingly stiff competition from Japan’s Komatsu and needed cost savings and productivity increases. In contract negotiations with the UAW in fall 1991, the company tried to institute more flexible work practices. The UAW had recently achieved a settlement with Caterpillar’s U.S. rival John Deere that gave the workers significant wage increases and higher health and pension benefits. Following the custom of UAW negotiations with the big three auto makers, the union expected a matching contract from Caterpillar. The company responded that it could not afford to follow the pattern of the UAW contract with Deere; whereas Deere served mostly the U.S. market, Caterpillar had a large export market with stiffer competition. The company offered smaller wage increases and wanted the workers to pay more for their health plans. It also wanted separate terms at each of its factories to suit the local needs. The union feared that this would increase the company’s bargaining power, pitting small local union branches against a large single employer. The union believed that the company could cut costs using productivity gains base...